MATH7016: Spring 2019, Week 4

VBA Assessment 1

VBA Assessment 1 will take place in Week 6 (5 & 8 March) in your usual lab time. You will not be allowed any resources – but the library of code (p.148) and these formulae will appear on the assessment:

You will be asked to write a program that takes as input all the problem parameters, perhaps some initial conditions, a step-size, and a final time, and implements Heun’s Method (or possibly Euler’s Method): similar to Exercise 1 on p. 122 (except possibly implementing Heun’s Method) and also Exercise 1 on p.128 (except without the “conditional” derivative).

If you can write programs for each of the four initial value problems above you will be in absolutely great shape for this assessment.

Q. 2: Using your Program [20%]

You will then be asked to use your program to answer a number of questions about your model. For example, assuming Heun’s Method is used, consider the initial value problem (3.7) on p. 119.

Given, , , , , approximate .

Given, , , , , investigate the behaviour of for large .

Given , , , , , run the Heun program. Comment on the behaviour of . Run the same program except with . Comment on the behaviour of .

Given, , , , , , run the Heun program. Comment on the behaviour of .

Week 4

We finished off a Three Term Taylor Method example and spoke again about Heun’s Method.